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Dependent interest and transition rates in life insurance


  • Buchardt, Kristian


For market consistent life insurance liabilities modelled with a multi-state Markov chain, it is of importance to consider the interest and transition rates as stochastic processes, for example in order to consider hedging possibilities of the risks, and for risk measurement. In the literature, this is usually done with an assumption of independence between the interest and transition rates. In this paper, it is shown how to valuate life insurance liabilities using affine processes for modelling dependent interest and transition rates. This approach leads to the introduction of so-called dependent forward rates. We propose a specific model for surrender modelling, and within this model the dependent forward rates are calculated, and the market value and the Solvency II capital requirement are examined for a simple savings contract.

Suggested Citation

  • Buchardt, Kristian, 2014. "Dependent interest and transition rates in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 55(C), pages 167-179.
  • Handle: RePEc:eee:insuma:v:55:y:2014:i:c:p:167-179
    DOI: 10.1016/j.insmatheco.2014.01.004

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    References listed on IDEAS

    1. Norberg, Ragnar, 2010. "Forward mortality and other vital rates -- Are they the way forward?," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 105-112, October.
    2. Ragnar Norberg, 1999. "A theory of bonus in life insurance," Finance and Stochastics, Springer, vol. 3(4), pages 373-390.
    3. Biffis, Enrico, 2005. "Affine processes for dynamic mortality and actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 443-468, December.
    4. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    5. Steffensen, Mogens, 2002. "Intervention options in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 71-85, August.
    6. Dahl, Mikkel & Moller, Thomas, 2006. "Valuation and hedging of life insurance liabilities with systematic mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 193-217, October.
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    Cited by:

    1. repec:gam:jrisks:v:6:y:2018:i:3:p:63-:d:154241 is not listed on IDEAS
    2. Jang, Jiwook & Mohd Ramli, Siti Norafidah, 2015. "Jump diffusion transition intensities in life insurance and disability annuity," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 440-451.
    3. Berdin, Elia & Gründl, Helmut & Kubitza, Christian, 2017. "Rising interest rates, lapse risk, and the stability of life insurers," ICIR Working Paper Series 29/17, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR).
    4. Marcus Christiansen & Andreas Niemeyer, 2015. "On the forward rate concept in multi-state life insurance," Finance and Stochastics, Springer, vol. 19(2), pages 295-327, April.
    5. Xavier Milhaud & Christophe Dutang, 2018. "Lapse tables for lapse risk management in insurance: a competing risk approach," Post-Print hal-01727669, HAL.
    6. Kristian Buchardt & Thomas Møller, 2015. "Life Insurance Cash Flows with Policyholder Behavior," Risks, MDPI, Open Access Journal, vol. 3(3), pages 1-28, July.

    More about this item


    Affine processes; Doubly stochastic process; Multi-state life insurance models; Policyholder behaviour; Solvency II; Surrender;

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies


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